Area and Dimensions: Quadratic Problems in Rectangles

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

The length of a rectangular swimming pool is twice its width. If the area of the pool is 288 square meters, find the dimensions of the pool using the quadratic formula.

• Width: 12 meters, Length: 24 meters

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 8 meters, Length: 16 meters

A rectangular field has a width of x meters and a length of (x + 4) meters. If the area of the field is 60 square meters, what are the possible values for x?

• 8

• 6

• 10

• 4

A rectangular poster has a length that is 5 inches longer than its width. If the area of the poster is 60 square inches, calculate the dimensions of the poster.

• Width: 5 inches, Length: 10 inches

• Width: 7 inches, Length: 12 inches

• Width: 4 inches, Length: 9 inches

• Width: 6 inches, Length: 11 inches

The area of a rectangular classroom is 120 square feet. If the length is 2 feet more than twice the width, find the dimensions of the classroom using the quadratic formula.

• Width: 6 feet, Length: 14 feet

• Width: 8 feet, Length: 18 feet

• Width: 7 feet, Length: 16 feet

• Width: 5 feet, Length: 10 feet

A rectangular plot of land has a width of x meters and a length of (2x - 3) meters. If the area of the plot is 45 square meters, determine the dimensions of the plot.

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 8 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 12 meters

A rectangular box has a length that is 4 inches longer than its width. If the area of the base of the box is 96 square inches, what are the dimensions of the base?

• Width: 8 inches, Length: 12 inches

• Width: 4 inches, Length: 8 inches

• Width: 10 inches, Length: 14 inches

• Width: 6 inches, Length: 10 inches

The length of a rectangular piece of land is 3 meters less than twice its width. If the area of the land is 50 square meters, find the width and length of the land.

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 10 meters

• Width: 7.5 meters, Length: 12 meters

A rectangular garden has a length of (x + 2) meters and a width of (x - 1) meters. If the area of the garden is 30 square meters, find the value of x and the dimensions of the garden.

• x = 2, Length = 4 meters, Width = 2 meters

• x = 3, Length = 5 meters, Width = 2 meters

• x = 4, Length = 6 meters, Width = 3 meters

• x = 5, Length = 7 meters, Width = 4 meters

A rectangular room has a length that is 6 feet longer than its width. If the area of the room is 72 square feet, calculate the dimensions of the room.

• Width: 8 feet, Length: 14 feet

• Width: 4 feet, Length: 10 feet

• Width: 6 feet, Length: 12 feet

• Width: 5 feet, Length: 11 feet